7.22.6 problem 16

Internal problem ID [581]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 5. Linear systems of differential equations. Section 5.1 (First order systems and applications). Problems at page 335
Problem number : 16
Date solved : Wednesday, February 05, 2025 at 03:45:52 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=8 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-2 x \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 35

dsolve([diff(x(t),t)=8*y(t),diff(y(t),t)=-2*x(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_1 \sin \left (4 t \right )+c_2 \cos \left (4 t \right ) \\ y \left (t \right ) &= \frac {c_1 \cos \left (4 t \right )}{2}-\frac {c_2 \sin \left (4 t \right )}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 42

DSolve[{D[x[t],t]==8*y[t],D[y[t],t]==-2*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1 \cos (4 t)+2 c_2 \sin (4 t) \\ y(t)\to c_2 \cos (4 t)-\frac {1}{2} c_1 \sin (4 t) \\ \end{align*}